Journal of Statistical Physics

, Volume 52, Issue 1–2, pp 479–487 | Cite as

Possible generalization of Boltzmann-Gibbs statistics

  • Constantino Tsallis
Short Communications


With the use of a quantity normally scaled in multifractals, a generalized form is postulated for entropy, namelyS q k [1 – ∑ i=1 W p i q ]/(q-1), whereq∈ℝ characterizes the generalization andpi are the probabilities associated withW (microscopic) configurations (W∈ℕ). The main properties associated with this entropy are established, particularly those corresponding to the microcanonical and canonical ensembles. The Boltzmann-Gibbs statistics is recovered as theq→1 limit.

Key words

Generalized statistics entropy multifractals statistical ensembles 


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    A. Rényi,Probability Theory (North-Holland, 1970).Google Scholar

Copyright information

© Plenum Publishing Corporation 1988

Authors and Affiliations

  • Constantino Tsallis
    • 1
  1. 1.Centro Brasileiro de Pesquisas Fisicas-CBPF/CNPqRio de Janeiro, RJBrazil

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